We shall discuss the antilinear \(\mathcal {CPT}\)  symmetry within a string theory context. It will be argued that the breaking of Lorentz symmetry by a homogeneous background related to the Kalb-Ramond [1]}, [2]} axion field will lead to \(\mathcal {CPT}\)  violation (CPTV). This CPTV background will be essential for producing leptogenesis in our model. Moreover quantum fluctuations of the axion will lead to the Kalb-Ramond axion being coupled to the axial anomaly expressed in terms of gauge fields in the model. We shall comment on the role of this axion as dark matter.
